Simplify the following expression: $ a = \dfrac{-8}{3} + \dfrac{6n}{-6n + 7} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-6n + 7}{-6n + 7}$ $ \dfrac{-8}{3} \times \dfrac{-6n + 7}{-6n + 7} = \dfrac{48n - 56}{-18n + 21} $ Multiply the second expression by $\dfrac{3}{3}$ $ \dfrac{6n}{-6n + 7} \times \dfrac{3}{3} = \dfrac{18n}{-18n + 21} $ Therefore $ a = \dfrac{48n - 56}{-18n + 21} + \dfrac{18n}{-18n + 21} $ Now the expressions have the same denominator we can simply add the numerators: $a = \dfrac{48n - 56 + 18n}{-18n + 21} $ $a = \dfrac{66n - 56}{-18n + 21}$ Simplify the expression by dividing the numerator and denominator by -1: $a = \dfrac{-66n + 56}{18n - 21}$